Question

5i / 3-4i division of the following

Answer 1

Answer:

$\frac{5i}{3 - 4i} = \frac{3i - 4}{5}$

Step-by-step explanation:

Given

$\frac{5i}{3 - 4i}$

Required

Solve

We have:

$\frac{5i}{3 - 4i}$

Rationalize

$\frac{5i}{3 - 4i} = \frac{5i}{3 - 4i} * \frac{3 + 4i}{3 + 4i}$

$\frac{5i}{3 - 4i} = \frac{5i(3 + 4i)}{(3 - 4i)(3 + 4i)}$

Apply difference of two squares on the denominator

$\frac{5i}{3 - 4i} = \frac{5i(3 + 4i)}{3^2 - (4i)^2}$

$\frac{5i}{3 - 4i} = \frac{5i(3 + 4i)}{9 - (16*-1)}$

$\frac{5i}{3 - 4i} = \frac{5i(3 + 4i)}{9 +16}$

$\frac{5i}{3 - 4i} = \frac{5i(3 + 4i)}{25}$

Divide common factor (5)

$\frac{5i}{3 - 4i} = \frac{i(3 + 4i)}{5}$

Expand the numerator

$\frac{5i}{3 - 4i} = \frac{3i + 4*-1}{5}$

$\frac{5i}{3 - 4i} = \frac{3i - 4}{5}$